Rainbow triangles in three-colored graphs
Combinatorics
2018-06-04 v1
Abstract
Erdos and Sos proposed a problem of determining the maximum number F(n) of rainbow triangles in 3-edge-colored complete graphs on n vertices. They conjectured that F(n) = F(a)+ F(b)+F(c)+F(d)+abc+abd+acd+bcd, where a+b+c+d = n and a, b, c, d are as equal as possible. We prove that the conjectured recurrence holds for sufficiently large n. We also prove the conjecture for n = 4k for all k. These results imply that lim F(n) n^3/6 = 0.4, and determine the unique limit object. In the proof we use flag algebras combined with stability arguments.
Cite
@article{arxiv.1408.5296,
title = {Rainbow triangles in three-colored graphs},
author = {Jozsef Balogh and Ping Hu and Bernard Lidicky and Florian Pfender and Jan Volec and Michael Young},
journal= {arXiv preprint arXiv:1408.5296},
year = {2018}
}
Comments
27 pages